Uniqueness of equilibrium states for some partially hyperbolic horseshoes

Alexander Arbieto; Luciano Prudente

doi:10.3934/dcds.2012.32.27

Article Contents

2012, Volume 32, Issue 1: 27-40. Doi: 10.3934/dcds.2012.32.27

This issue Previous Article Lipschitz regularity of solution map of control systems with multiple state constraints Next Article Transversal intersections of invariant manifolds of NMS flows on $S^{3}$

Uniqueness of equilibrium states for some partially hyperbolic horseshoes

Alexander Arbieto^1, and
Luciano Prudente^1,

1.
Instituto de Matemática - UFRJ, Av. Athos da Silveira Ramos 149, Cidade Universitária - Ilha do Fundão, P.O. Box 68530. Rio de Janeiro - RJ

Received: June 30, 2010

Revised: April 30, 2011

Published: December 2011

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Abstract

In this note, we consider a partially hyperbolic horseshoe and prove uniqueness of equilibrium states for a class of potentials. In particular we obtain that there exists a unique maximal entropy measure.

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Mathematics Subject Classification: Primary: 37D35; Secondary: 37D30.

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